X3849

X524com(5th EULER TRIANGLE)

X3849 = infinite point of Brocard axis of the 3rd pedal triangle of X6
< A B C >: Reference Triangle △ABC [ A B ]: Sideline AB (Base c = 1) [ B C ]: Sideline BC (Side a) [ C A ]: Sideline CA (Side b) { 2, 187 }: Central Line L(2, 187) { 30, 511 }: Central Line L(30, 511) { 385, 671 }: Central Line L(385, 671) { 381, 2080 }: Central Line L(381, 2080) { 597, 2030 }: Central Line L(597, 2030) { 325, 2482 }: Central Line L(325, 2482) A = Vertex A (0.0000, 0.0000) B = Vertex B (1.0000, 0.0000) C = Vertex C (0.6122, 0.5999) X_2 = CENTROID (0.5374, 0.2000) X_187 = INVERSE-IN-CIRCUMCIRCLE OF X(6) (SCHOUTE CENTER) (1.1986, 1.2559) X_30 = EULER INFINITY POINT (0.7469, 0.7481) X_511 = ISOGONAL CONJUGATE OF X(98) (0.2335, -0.3020) X_385 = -HIRST INVERSE OF X(6) (2.2863, 2.0795) X_671 = TRILINEAR POLE OF LINE X(2)X(523) (0.9639, -0.0323) X_381 = MIDPOINT OF X(2) AND X(4) (0.5748, 0.2979) X_2080 = INVERSE-IN-CIRCUMCIRCLE OF X(182) (1.8972, 2.4097) X_597 = MIDPOINT OF X(2) AND X(6) (0.5687, 0.2336) X_2030 = RADICAL TRACE OF MOSES CIRCLE AND CIRCUMCIRCLE (0.8993, 0.7615) X_325 = -HIRST INVERSE OF X(69) (-0.3370, -0.7398) X_2482 = STEINER-INELLIPSE-ANTIPODE OF X(115) (0.3242, 0.3161) X_3849 = com(5th EULER TRIANGLE) (0.8489, 0.6973) A B C X2 X187 X30 X511 X385 X671 X381 X2080 X597 X2030 X325 X2482 X3849 (a, b, c) = (5, 6, 7) | AB = 1

X3849 (X524com(5th EULER TRIANGLE)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

Barycentrics: \(f(a,b,c) : f(b,c,a) : f(c,a,b)\), where \(f(a,b,c) = 4a^{4} - 2b^{4} - 2c^{4} - a^{2}b^{2} - a^{2}c^{2} + 2b^{2}c^{2}\)
▸ Incident Central Lines8 lines

{2, 187}, {30, 511}, {325, 2482}, {381, 2080}, {385, 671}, {597, 2030}, {599, 3734}, {1992, 2549}

▸ Functional Relations2 relations